Theorems · Theorem · field theory
Polynomial.coeff_map
∀ {R : Type u} {S : Type v} [inst : Semiring R] {p : Polynomial R} [inst_1 : Semiring S] (f : R →+* S) (n : ℕ),
(Polynomial.map f p).coeff n = f (p.coeff n)- Defined in
- Mathlib.Algebra.Polynomial.Eval.Coeff
- Cited by
- 114 results in Mathlib
- Foundations
- Depth 106 from the axioms, rests on 1,835 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xproof · cited by 1,639
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffstatement and proof · cited by 1,045
- RingHom.compproof · cited by 899
Cited by114
Results whose statement or proof uses this declaration.
- Polynomial.map_mapproof · cited by 75
- Polynomial.map_injectiveproof · cited by 27
- Polynomial.Monic.natDegree_mapproof · cited by 21
- Polynomial.derivative_mapproof · cited by 17
- Polynomial.map_idproof · cited by 15
- Polynomial.degree_map_eq_of_leadingCoeff_ne_zeroproof · cited by 9
- Polynomial.leadingCoeff_map_of_injectiveproof · cited by 8
- Polynomial.degree_map_leproof · cited by 7
- Polynomial.map_expandproof · cited by 7
- Polynomial.map_toSubringproof · cited by 6
- Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zeroproof · cited by 5
- NumberField.Embeddings.finite_of_norm_leproof · cited by 4